I would eliminate MKB from your list of options. Their internet banking package is very unreliable in my experience. The system relies on an intricate password based authorisation and floppy disc "key". When that goes wrong, very few people at the branch speak English, and those that do ask you to call the computer services company that supports the banks server!
I opened an account with CIB Bank in 06 find their internet banking good their staff have good English BUT i find their fees a little hard to take compaired with Irish banks is this the same with all Hungarian banks ?